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**Published:** Jan 1953

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**Source: **STP139-EB

The concept that individual differences exist in all manufactured and natural products is not new, but a convenient method of studying, controlling, and predicting these differences has not been generally adopted in most engineering design and manufacturing. We have gradually been forced to accept the fact that our products cannot all be exactly alike, and we have therefore established limits or ranges within which the characteristics of the manufactured product will vary when the product is used or operated under a given set of conditions. For instance, we say that the temperature rise of a motor will be no greater than 55 C when operated at full load, or that the minimum life of an incandescent lamp will be 1000 hr. Since it is the variation in individual properties which determines such factors as average, minimum, and maximum values, it is obvious that some generally recognized scheme for describing variations is extremely useful in engineering, manufacturing, and testing. Various schemes have been and are currently being used for the description of variation. One widely used system merely states the approximate maximum and minimum values which a product may have. Another scheme states the average difference between the individual values and the numerical average. The most generally used scheme defines the variation as the root mean square of the individual deviations from the average, this being preferred over other schemes since it can be used to advantage in predicting the number of values which will be found between two specified limits and furnishes a basis for accurate estimates of the error one makes when sampling or inspecting only a small part of the total population. This measure of variation is called the standard deviation of the values from the average and is usually represented by the Greek letter sigma, σ. Since the arithmetic calculation of sigma is usually rather time consuming, graphical methods are faster and will be discussed to show their general usefulness in engineering and test work. Another important use of the graphical method has to do with the basic idea that all data which one may collect by tests on a manufactured product, or on almost any other activity one might choose to examine, are merely samples. The information which may be obtained from this sample is limited in its exactness due to sampling variations or error but may be made more exact as the size of the sample is increased. Unfortunately this increase in information is not proportional to the amount of data collected. The use of the graphical method enables one to determine easily and quickly the error between the sample and the true situation and gives a basis for determining whether the cost of additional sampling is commensurate with the increase in accuracy.

**Author Information:**

Schmidt, P. L.*Westinghouse Electric Corp., East Pittsburgh, Pa.*

**Committee/Subcommittee:** D12.12

**DOI:** 10.1520/STP46774S